Super Mario Galaxy 2 had a pretty good "1.5-player mode", where the second player controlled an invincible Luma who could shoot star bits at enemies to stun them. They could also literally shake them down for more, which in retrospect was hilarious.

Ricochet Infinity (a very good and advanced brick breaker game) had a mode like this – second player will receive control of the ball-mounted turret and can shoot at bricks.